All S.Qs of Chapter#03: Laws and Functions of Thermodynamics of Quantum Mechanics-II. We have arranged all S.Qs for BS/MSc Physics students.
Q.1 Define temperature of inversion? What is its value for hydrogen and helium?
Answer: The temperature at which Joule-Thomson coefficient is zero and changes sign is known as the temperature of inversion. For hydrogen its value is -80oCand for helium it is 35K.
Q.2 What are advantages of adiabatic demagnetization?
Answer: Adiabatic demagnetization is used to produce low temperature. A paramagnetic crystal is cooled to about 1K with the help of liquid helium. It is then subjected to a strong magnetic field. The heat produced during process of magnetization is conducted away by liquid helium. Then the magnetic field is removed adiabatically. This lowers the temperature of the crystal to about 0.005K.
Q.3 What is throttling process?
Answer: The process in which a compressed gas expands adiabatically on passing through a porous plug or throttle is called throttling process.
Q.4 What is effect of pressure on melting point of solids?
Answer: The Clapeyron equation is
The change in pressure due to change in temperature of melting point of a solid dT is given by above equation.
Q.5 Do all substances get cooled on adiabatic expansion?
Answer: No, all substances do not get cooled on adiabatic expansion. The change in temperature dT due to change in volume dV on adiabatic expansion is,
$$dT=-\frac{T\beta p}{C_v}dV$$
where β is coefficient of pressure at content volume. Only those substances for which β>0 show a cooling effect on adiabatic expansion.
Q.6 What is meant by cryogenics?
Answer: Cryogenics is the study of the production and behavior of materials at very low temperatures. A person who studies elements that have been subjected to extremely cold temperatures is called cryogenics. Cryogenicist use the Kelvin or Rankin temperature scales.
Q.7 What are thermodynamic potentials? Why they are called so?
Answer: The thermodynamics functions internal energy, Helmholtz free energy, enthalpy and Gibb’s free energy are called thermodynamic potentials. The behavior of these functions is similar to potential energy in mechanics that is why these are called thermodynamic potentials. For example, direction of isothermal-isochoric process is to make Helmholtz free energy minimum. In isothermal-isobaric process Gibbs free energy tends to be a minimum. In an isobaric-adiabatic process the enthalpy tends to be minimum.
Q.8 Why only four thermodynamic variables are defined?
Answer: The state of a system can be completely described by any four of five variables $p;\ v;\ T;\ S$ and u. Out of these u is determined remaining four variables as explained below:From first and second laws of thermodynamics,
$$dQ\ =du\ +\ pdv\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ dQ\ =\ TdS\ \ \ \ \ \ \ \ \ \ \ \ \$$
$$\Rightarrow\ du\ +\ pdv\ =TdS\ \ \ \ \ \Rightarrow\ du\ =\ TdS-\ pdv$$
Thus u can be determined and we are left with state variables $p;\ v;\ T;\ S$ This is why only four thermodynamics variables are defined.
Q.9 Discuss how the boiling point of liquid is affected by change of pressure?
Answer: The Clapeyron equation is
$$\frac{dp}{dT}=\frac{L}{T(V_2-V_1)}$$
The change is pressure due to change in temperature of melting point of a solid dT is given by above equation
If $V_2>V_1$ (as is practically), then $\frac{dp}{dT}>0$. This shows that boiling point of a liquid is always raised by increase of pressure.
Q.10 Show that Cv is independent of volume at a given temperature.
Answer: For an ideal gas,
$$pV=nRT\ \ \ \ \ \ \ \ \ \ \ \Rightarrow p=\frac{nRT}{V},\ \ \ \ \ \ \ \ \ \frac{\partial p}{\partial T}=\frac{nR}{V},\ \ \ \ \ \ \ \ \frac{\partial^2p}{\partial T^2}=0$$
Now,
$$\left[\frac{\partial C_V}{\partial V}\right]_T=T\left[\frac{\partial^2p}{\partial T^2}\right]_V=0\$$
Hence at a given temperature, $C_V$ is independent of temperature for an ideal gas. Same is the case for real gas.
Q.11 By which process lowest temperature can be achieved?
Answer: The process by which lowest temperature can be achieved is called adiabatic demagnetization.
Q.12 Which quantity is constant in Joule-Thomson expansion?
Answer: The quantity which remains constant in Joule-Thomson expansion is called enthalpy.
Q.13 On what factors cooling produced due to adiabatic demagnetization depends upon?
Answer: The cooling produced due to adiabatic demagnetization depends upon initial temperature and intensity of magnetic field.
